1. Mathematics (9-1) - iGCSE
Year 09
Unit 07 – Answers

2. 7 - Prior knowledge check
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400
a b c. 5.0
a b
Teaspoon 5ml, drink can 300ml, bucket 5 litres, juice carton 1 litre.
a. 520cm b. 240mm c. 1000mm d. 3410m e. 327ml f. 2,4 litres

3. 7 - Prior knowledge check
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a. 18 b c. 480 d. 2
a. x = 1 c y b. x = a bz c. x = 2𝑚 y
Suitable circle with correct centre, radius and diameter labelled.

4. 7 - Prior knowledge check
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a b. 108cm2

5. 7 - Prior knowledge check
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a b. c. 48cm3

6. 7 - Prior knowledge check
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40cm2
370cm3
Students' own answers. The boxes will fit exactly into a cuboid box with dimensions 9cm x 12cm x 12cm.

7. 7.1 – Perimeter and Area a. 12cm2,16cm b. 30cm2, 30cm c. 96cm2, 44cm
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a. 12cm2,16cm b. 30cm2, 30cm c. 96cm2, 44cm
a. 1 = 4 b. 1 = 12 c. z = 5
a. Area = 46.5 m2, perimeter = 29m b. 1548mm2 c mm2
a. 60cm2 b. 30cm c. 26.6m2 d cm2
Area = 276cm2, perimeter = 72cm

8. 7.1 – Perimeter and Area
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£34.93
4350 m2
a. 96 = (9 + 15)h b. 96 = 12h c. h = 8cm
4cm
a. a = 6cm b. b = 2.8m (1 d.p.)
100cm

9. 7.2 – Units and Accuracy a. 3.6 b. 320 c. 8.50 d. 15.7
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a b c d. 15.7
a. i. 2.5 kg ii kg iii kg b. i. 2m ii. 38m iii. 42m
a. 1 cm = 10 mm, so they have same side length
1cm2 and 100mm2
1 cm2 = 100 mm2
a. Suitable sketch of the squares
1m2 = 10000cm2
Divide by 10000

10. 7.2 – Units and Accuracy
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a. 2.5cm2 b cm2 c. 0.7m2 d. 340mm2 e. 88,500cm2 f cm2 g. 370,000mm2 h. 2.8m
a. 0.6m2 b. 544 mm2 c. 468mm2 d cm2
24.2 ha
1,600,000
a. 33 mm, 27 m b. 27mm ≤ length ≤ 33mm

11. 7.2 – Units and Accuracy
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19g ≤ mass ≤ 21g
a. i. 35.5cm ii cm
a. 17.5m ≤ x ≤ 18.5 m b kg ≤ x ≤ kg c m ≤ x ≤ 1.45 m d km ≤ x ≤ km

12. 7.2 – Units and Accuracy
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a. i. 7.5cm ii. 8.5cm b. i. 5.25kg ii. 5.35kg c. i m ii m d. i litres ii litres e. i. 4500m ii. 5500m f. i. 31.5mm ii. 32.5mm g. i kg ii kg

13. 7.2 – Units and Accuracy a. 14.5cm, 15.5cm, 27.5cm, 28.5cm
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a. 14.5cm, 15.5cm, 27.5cm, 28.5cm
Lower bound 84cm, upper bound 88cm
Upper bound m2, lower bound m2
a. Height 6.15cm, 6.25cm; area 23.5cm2, 24.5cm2
i ii (2 d.p.)
3.98cm (2 d.p.)

14. 7.3 – Prisms 72cm3 a. b = 8 b. h = 4 a. Students’ own sketch
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72cm3
a. b = 8 b. h = 4
a. Students’ own sketch
c. Areas are 20cm2, 28cm2 and 35cm2.The identical pairs are (top,bottom) (front,back) and (left side,right side)
Surface area is 166cm2
72cm

15. 7.3 – Prisms
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a. Yes, because it has the same cross section all along its length,
12 cm2
72cm3, same value as for volume calculated in Q1.
a. 80 cm3 b. 204 cm3
a. 4cm b. 108cm2
4cm

16. 7.3 – Prisms a. Suitable sketch of cube 1 cm3 = 1,000mm3
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a. Suitable sketch of cube
1 cm3 = 1,000mm3
Divide by 1,000
a. 1m3 and 1,000,000cm3
Multiply by 1,000,000
a. 4,500,000cm3 b. 52,000mm3
9.5 m3 d cm3
5.2 litres f cm3
75cm3 h litres
a m2 b. 3

17. 7.3 – Prisms
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9.2cm
a m3
Estimated volume of leaf mould in wood is x 0.2 = 4000 m = 80,000,12 x 80,000 = 960,000 worms
Volume = x 4x x 2x x 5x = 20x3
Upper bound: 5.5 x 3.5 x 8.5 = cm3, Lower bound: 4.5 x 2.5 x 7.5 = cm3

18. 7.4 – Circles a. r = 5 b. r = ± 5 a. x = y m b. x = ±t c. x = ± 𝑝
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a. r = 5 b. r = ± 5
a. x = y m b. x = ±t c. x = ± 𝑝
a. All ratios are 3.14 to 2 d.p. b
a cm b m c mm
a cm2 b. 4.5 m2 c m2
5 boxes
a mm b mm2
Circumference = 201cm, = 497

19. 7.4 – Circles
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a. 10πcm, 25πcm2 b. 14πcm, 49πcm2 c. 20πcm, 100πcm2 d. 24πcm, 144πcm2
a. i. area 36πcm, circumference 12πcm ii. 110cm2 (2 s.f.), 38cm
The answers in terms of π because they have not been rounded
a. 104 = πd b. d = 33.1cm
3.8 cm (1 d.p.)

20. 7.4 – Circles a. 12.87 m b. 28.3 cm a. A π = r2 b. A π = r
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a m b cm
a. A π = r2 b. A π = r
X: 3.6cm Y: 2.8 cm Z: 4.7 cm
8 x 66 circles = 528 Total area of circles = 528 x 9π = 14,929cm2 (to nearest cm2) Area thrown away = 20,000 – 14,929 = 5071cm2 Percentage thrown away = = 0.25 or 25%

21. 7.5 – Sector of Circles a. 16πcm, 64πcm2 b. 50.3 cm, 201 cm2
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a. 16πcm, 64πcm2 b cm, 201 cm2
a. 4π b. 2π c. 3π + 7
a. i. 18πcm2 ii cm2 b. i. 25πcm2 ii cm2
a. i. (3π + 6) cm ii cm b. i. (5π + 10)cm ii cm
a. (16π +16)cm b cm
a. 4.4m2 b. 8.8m
21.5 cm2
a cm b. 3.1cm
58.9 cm

22. 7.5 – Sector of Circles Arc length = 7.85cm, perimeter = 37.9cm
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Arc length = 7.85cm, perimeter = 37.9cm
a cm, 85.5cm2 b cm2 ≤ area < 98.2 cm2
a. 10 = x 360 x π x 32 b. 127° (to the nearest degree)
74°
8.56 m
5.0 cm (1 d.p.)
(16π - 32) cm2

23. 7.6 – Cylinders & Spheres Students’ sketches
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Students’ sketches
a. ±6 b c. ±1.6 d. 2.2
a. πr2 b. V = πr2h
a. 197cm3 b. 167,283.5 mm3
0.267 m3
3.2 cm
a cm2 b. 16,889.2mm2 c. 41.3m2
26 mm
300cm3

24. 7.6 – Cylinders & Spheres
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a. SA = 324πmm2, V = 972πmm3 b. SA = 100πcm2, V = 500π 3 cm3
191 mm3 ≤ volume ≤ 348mm3
a. Total volume = π = 1140mm3 (3 s.f.) b. Total SA = 208π = 653mm2
17mm
6.31m
3.1cm

25. 7.7 – Spheres & Composite Solids
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a. 20 cm2 b. 21cm2
9.4 cm
a. Net of square-based pyramid, square 4cm side, height of each triangle 6cm
Triangular face 12cm2, square 16cm2
64cm2
213 cm3
a. i. = 8.7 cm (1 d.p.) b. Total volume = 950 cm3

26. 7.7 – Spheres & Composite Solids
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a. 96πcm3 b. 302cm3
a. 257πcm2 b. 657πcm2 c. 907πcm2
l = = 9.85cm (2 d.p.), area = cm2
Volume = 63,363mm3 (to nearest mm3) Surface area = 9,694 mm2 (to nearest mm2)
10.6cm

27. 7.7 – Spheres & Composite Solids
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Radius of sphere = cm, height of cone = 20.9cm
Volume of whole cone = 144π, volume of smaller cone = π Volume of frustum = π
a. 10πx3 b. 20πx2 c. 10πx3 + 20πx2 = 10πx2(x + 2)
51π = 160cm3 (3 s.f.)

28. 7 – Problem-Solving
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6.6cm
8.6cm
72.2%
£935.03
864 cm3

29. 7 – Problem-Solving
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a. 9.5 cm3 b. 25cm
7cm
a. 50.3cm b. 64π = 201.1cm2
25.7cm
a. 15,7cm2 b. 5.2cm
a. 40,000cm2 b. 0.56m2 c. 9.5m3 d. 3000ml – 3000cm3

30. 7 – Problem-Solving 9.5 cm3 ≤ volume < 105cm3
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9.5 cm3 ≤ volume < 105cm3
a m ≤ 36m < 36.5m b. 9.15cm ≤ 9.2cm < 9.25cm c km ≤ 23.6km < 23.65km
36cm3
492.9 cm2
36πcm3
301.6cm3
Students‘ own answers

31. 7 – Strengthen 2D Shapes a. 2cm b. 10.3cm
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2D Shapes
a. 2cm b. 10.3cm
a. 55 = 1 2 (7 + b) x 10 b. 55 = b c. b = 4cm
a. i. 4πcm ii. 12.6cm b. i. 12πcm ii. 37.7cm
a. 2πr = 19.5cm, πr2 = 342 b. A = πr2 c. C = 2πr
a. i. 4πcm2 ii. 12.6cm2 b. i. 36πcm2 ii cm2

32. 7 – Strengthen
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a cm2 b. 77.0cm2 c. 44.0cm d. 50.3cm e. 14.0cm f cm
a b c = 5 8
a b cm2 c. 25.1cm2 d. 50.3cm e. 6.3cm f. 16cm g. 22.3cm

33. 7 – Strengthen Accuracy and Measures
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Accuracy and Measures
a. 10,000cm2, 20,000cm2 b. cm2 10,000 cm2 x10, ÷10,000 m m2
a. 1,000,000cm3, 2,000,000cm2 b. cm2 10, cm2 x1,000, ÷1,000, m m2
a. 2.5 b and c ≤ 25 ≤ 27.5
a ≤ l < 23.5 b ≤ l ≤ 32.5

34. 7 – Strengthen
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3D Solids
a. 60cm3 b. 63cm3 c. 240π = 754cm3
a. Students’ sketches b. i cm2 ii. 37.7cm iii cm2 iv cm2

35. 7 – Strengthen
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a. Volume = 340 cm3 = 4 3 πr3, surface area = 746 cm2 = 4πr2 b. Surface area = 4πr2 c. Volume = 4 3 πr2 d. i cm ii cm3
a. 4cm b. 5cm c cm3 d. 75.4cm2

36. 7 – Extend
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a cm2
a. 50xy b. 500xyz
a. Split the garden with a line parallel to the wall to form a rectangle and a right- angled triangle. The hypotenuse of the triangle is 5 m. The right hand side of the triangle is = 3m. These are two sides of a Pythagorean triple, so the third side is 4m. This side is the same length as the wall, so the wall is 4 m long,
Area of lawn = 38 m2; 2 bottles
201m

37. 7 – Extend
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Capacity of tank = 942,477.8 cm3 = 942,477.8 ml Time to fill = 3,142 seconds = 52 minutes
a. Shade rectangle a by x b. Shade rectangle a by x and rectangle b by x c. Shade one of the end triangles
a. 3.5cm b. 28 cm2
Area of trapezium = (a + b)h So 144 = ((x - 6) + (x + 2)) x 3x = (2x - 4) x 3x 144 = (x - 2) x 3x Therefore 3x2 - 6x = 144

38. 7 – Extend
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6 litres 3x
a b c d
a b c
3.85 x 1013m2

39. 7 – Unit Test
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Sample student answer
The question asks for the answer correct to 3 s.f. The student has rounded to 4 s.f. Although all the maths is correct they must make sure they write the answer in the requested way